A slew of high-profile warnings about expected damage to the UK economy if Britain votes to quit the bloc on June 23 had put the Leave camp on the back foot with just under a month to go.

But with voters' fears over immigration seen as their best hope of shifting opinion - with polls giving Remain a consistent lead - Mr Johnson urged people to "take back control".

The Tory MP and former London mayor accused David Cameron of repeatedly breaking promises to secure restrictions on free movement and said the present system did not enjoy public "consent".

"We are adding a population the size of Oxford to the UK every year just from EU migration," he said after the publication of the Office for National Statistics data.

He insisted he had not abandoned his view that immigration brought " great benefits" to the country but said pressure on public services had to be addressed.

"The system has spun out of control. We cannot control the numbers. We cannot control the terms on which people come and how we remove those who abuse our hospitality," he said.

"This puts huge pressure on schools, hospitals and housing. It is exploited by some big companies that use immigration to keep wages down."

The Government had failed in its target to reduce net migration to the tens of thousands " because of the simple reality that inside the EU we cannot control immigration", he said.

"Even worse, the Prime Minister's deal has given away control of immigration and asylum forever.

"His deal does nothing to solve this crisis and has not brought back a single power for the UK. The rogue European Court now controls not just immigration policy but how we implement asylum policy under the Charter of Fundamental Rights.

"And, on top of all of this, new countries are in the queue to join the EU and the EU is extending visa-free travel to the border of Syria and Iraq. It is mad.

"If you vote in on June 23, you are kissing goodbye permanently to control of immigration."

Ukip leader Nigel Farage said: "Mass immigration is still hopelessly out of control and set to get worse if we remain inside the EU, going on with disastrous open borders.

"However I don't believe these official figures and I'm sure the real numbers are much higher."

Mr Johnson sought to play down warnings of an post-Brexit economic shock - joined yesterday by the World Trade Organisation and the Institute for Fiscal Studies.

"We are hearing an awful lot of stuff from the Remain side that I think is starting to lose any touch with credibility whatsoever," he told Sky News.

"They are going on and on about the downsides to such an extent that I fear they are starting to talk the UK down."

The "best authority" was Mr Cameron who had said before the campaign that there "would be an awful lot of scaremongering but actually Britain could prosper perfectly well", he said.

London Mayor and Remain campaigner Sadiq Khan said people had legitimate concerns about immigration.

"You can either try to address people's fears, or play on them. I believe in addressing them. You've got to hear what people are saying, they are legitimate concerns people have."

A Downing Street spokesman said: "Of course people rightly have concerns on immigration but the PM's view is very clearly that wrecking the economy and destroying jobs by getting rid of our privileged access to the world's biggest market is not the answer.

"Our new special status in Europe now means that EU citizens will now have to put something in before they get something out in welfare.

"And we don't know what would happen to migration if we were to leave the EU. Those who want to leave are telling one group of people that they will cut migration while telling other groups that they will keep freedom of movement or increase visas."

He was unable to give an indication what impact on EU migration to the UK could be expected as a result of benefit curbs agreed as part of the Prime Minister's renegotiation with Brussels.

A record number of deportations "is a sign of having control of our borders", he said.

Labour former home secretary Jacqui Smith: "The latest figures show over 250,000 EU nationals work in our public services, so let's not throw the baby out with the bath water.

"We can have a fair immigration system, where those who work hard and pay their taxes are welcome, without trashing our economy.

"Vote Leave know they have lost the argument on the economy, which is why they are dancing to Nigel Farage's tune and focusing elsewhere.

"They have serious questions to answer about whether they are proposing more non-EU migration and what happens to those Britons currently living and working in Europe.